Pembahasan Soal Ujian Profesi Aktuaris
| Institusi |
: |
Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian |
: |
Metoda Statistika |
| Periode Ujian |
: |
November 2017 |
| Nomor Soal |
: |
4 |
SOAL
Untuk suatu table double decrement, diketahui
- \(q_x^{‘\left( 1 \right)} = 0,2\)
- \(q_x^{\left( 2 \right)} = 0,3\)
- Setiap decrement terdistribusi secara uniform dalam masing-masing tabel single decrement yang diasosiasikan.
Hitunglah \(q_x^{\left( 2 \right)} = 0,3\) (dibulatkan 3 desimal).
- 0,089
- 0,126
- 0,144
- 0,167
- 0,192
| Diketahui |
- \(q_x^{‘\left( 1 \right)} = 0,2\)
- \(q_x^{\left( 2 \right)} = 0,3\)
- Setiap decrement terdistribusi secara uniform dalam masing-masing tabel single decrement yang diasosiasikan.
|
| Rumus yang digunakan |
\(q_x^{\left( 1 \right)} = q_x^{‘\left( 1 \right)}\left[ {1 – \frac{1}{2} \cdot q_x^{‘\left( 2 \right)}} \right]\)
\(q_x^{\left( 2 \right)} = q_x^{‘\left( 2 \right)}\left[ {1 – \frac{1}{2} \cdot q_x^{‘\left( 1 \right)}} \right]\) |
| Proses pengerjaan |
\(q_x^{\left( 1 \right)} = q_x^{‘\left( 1 \right)}\left[ {1 – \frac{1}{2} \cdot q_x^{‘\left( 2 \right)}} \right]\)
\(= q_x^{‘\left( 1 \right)}\left[ {1 – \frac{1}{2} \cdot \left( {\frac{{q_x^{\left( 2 \right)}}}{{1 – \frac{1}{2} \cdot q_x^{‘\left( 1 \right)}}}} \right)} \right]\)
\(= 0,2\left[ {1 – \frac{1}{2}\left( {\frac{{0,3}}{{1 – \frac{{0,2}}{2}}}} \right)} \right]\)
\(= 0,16666667\) |
| Jawaban |
d. 0,167 |
